Department of Psychology, National University of Singapore, Singapore, Singapore.
Department of Statistics, Duksung Women's University, Seoul, Korea.
Multivariate Behav Res. 2020 Jan-Feb;55(1):30-48. doi: 10.1080/00273171.2019.1598837. Epub 2019 Apr 25.
Extended redundancy analysis (ERA) combines linear regression with dimension reduction to explore the directional relationships between multiple sets of predictors and outcome variables in a parsimonious manner. It aims to extract a component from each set of predictors in such a way that it accounts for the maximum variance of outcome variables. In this article, we extend ERA into the Bayesian framework, called Bayesian ERA (BERA). The advantages of BERA are threefold. First, BERA enables to make statistical inferences based on samples drawn from the joint posterior distribution of parameters obtained from a Markov chain Monte Carlo algorithm. As such, it does not necessitate any resampling method, which is on the other hand required for (frequentist's) ordinary ERA to test the statistical significance of parameter estimates. Second, it formally incorporates relevant information obtained from previous research into analyses by specifying informative power prior distributions. Third, BERA handles missing data by implementing multiple imputation using a Markov Chain Monte Carlo algorithm, avoiding the potential bias of parameter estimates due to missing data. We assess the performance of BERA through simulation studies and apply BERA to real data regarding academic achievement.
扩展冗余分析（ERA）结合了线性回归和降维，以简洁的方式探索多组预测因子和结果变量之间的定向关系。它旨在从每一组预测因子中提取一个成分，使其能够解释结果变量的最大方差。在本文中，我们将 ERA 扩展到贝叶斯框架中，称为贝叶斯 ERA（BERA）。BERA 的优点有三。首先，BERA 能够基于从马尔可夫链蒙特卡罗算法获得的参数的联合后验分布中抽取的样本进行统计推断。因此，它不需要任何重采样方法，而这是（频率派的）普通 ERA 测试参数估计的统计显著性所必需的。其次，它通过指定信息量大的先验分布，将从先前研究中获得的相关信息正式纳入分析。第三，BERA 通过使用马尔可夫链蒙特卡罗算法进行多次插补来处理缺失数据，避免了由于缺失数据导致的参数估计的潜在偏差。我们通过模拟研究评估了 BERA 的性能，并将 BERA 应用于关于学业成绩的真实数据。
